Optimal pricing, i.e., determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on the location of stores, for example. As the randomization frequently occurs at the municipal level, standard difference-in-differences methods may also fail. Possible solutions are based on methodologies to measure the effects of treatments on a single (or just a few) treated unit(s) based on counterfactuals constructed from artificial controls. For example, for each city in the treatment group, a counterfactual may be constructed from the untreated locations. In this paper, we apply a novel high-dimensional statistical method to measure the effects of price changes on daily sales from a major retailer in Brazil. The proposed methodology combines principal components (factors) and sparse regressions, resulting in a method called Factor-Adjusted Regularized Method for Treatment evaluation (\texttt{FarmTreat}). The data consist of daily sales and prices of five different products over more than 400 municipalities. The products considered belong to the \emph{sweet and candies} category and experiments have been conducted over the years of 2016 and 2017. Our results confirm the hypothesis of a high degree of heterogeneity yielding very different pricing strategies over distinct municipalities.
翻译:最优化定价,即确定某一产品利润或收入最大化的价格水平,是零售业的一项重要任务。要选择这样一个数量,首先需要从产品需求中估算价格弹性。回归方法通常无法恢复这种弹性,因为影响混乱和价格内在性。因此,通常需要随机化实验。然而,弹性可能因商店所在地不同而有很大差异。由于市一级经常发生随机化,标准差异差异方法也可能失败。可能的解决办法基于一种方法,根据人为控制所构建的反事实,对单一(或少数)处理单位的处理效果进行估测。回归方法通常无法恢复这种弹性。例如,对于治疗组中的每个城市,都可以从未经处理的地点建立反常的实验。在本文中,我们采用了一种新型的高尺度统计方法,以衡量巴西主要零售商每日销售价格变化的影响。拟议的方法将一个单一(或仅几个)处理单位的处理方法作为衡量方法,根据人工控制所构建的反常态性结果衡量一个单一(或低位)单位的处理结果。在正常水平上,对常规销售产品进行了一种不同的分析方法。我们采用了一种新的高位统计统计方法,对巴西的处理方法,对一个不同程度进行了分级分析。在正常销售结果中,结果进行了不同的分析。